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Space and Time Invariance (Classical Wave Equation)

  1. Apr 15, 2010 #1
    Hey, I've come across a part in my notes which I can't figure out. Essentially it says:

    [tex]\frac{\partial^{2}y}{\partial t^{2}}[/tex] = v[tex]^{2} [/tex] . [tex]\frac{\partial^{2}y}{\partial x^{2}}[/tex] is space and time invariant.

    Whereas:

    [tex]\frac{\partial y}{\partial t}[/tex] = -v . [tex]\frac{\partial y}{\partial x}[/tex] is not.

    Why is this the case?

    Cheers,
    Andrew
     
  2. jcsd
  3. Apr 16, 2010 #2
    Try putting a simple wave like y(x,t) = sin(x+vt) into both equations and see what happens.

    Guessing at equations is a standard way for physicists to explore a problem.
     
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